This paper aims to conduct the free vibration analysis of single-layer and laminated composite plates with multiple cutouts based on the scaled boundary finite element method (SBFEM) incorporated with the precise integration method (PIM) and the technique of the degree of freedom transform. It is applicable to a variety of shaped plates containing cordiform, circular and other complicated cutouts. The key equations are formulated built on the two-dimensional model, and the discretization is carried out in terms of only three translational displacement components as the basic unknowns. The high-order spectral elements are applied in the proposed technique to accurately simulate the arc boundaries of cutouts. Characterized by the important semi-analytical feature of the SBFEM, responses of the transverse free vibration are accurately explored. The derivation of governing equations strictly follows the 3D theory of elasticity without introducing any assumptions. The general solution of the SBFEM key equation is in the form of the matrix exponent, which is calculated by the PIM. As a type of highly precise approach, the PIM is introduced to create the global stiffness matrix from the analytical exponential matrix, which can make sure the eigensolutions with enough accuracy. Aided by the methodology of the kinetic energy formula, the global mass matrix of the perforated plate structure is constructed. According to the thin plates, the degree of freedom transform is employed to lower the dimensions of eigenvalue equation and thus improve the computational efficiency. Numerical examples of flexible square and circular plates with various cutouts reveal that excellent agreement is achieved between the natural frequencies predicted by the developed method and those from other methods and exact solutions. Furthermore, the effect of boundary conditions, skew angles, thickness-to-length ratios and sizes of cutouts on distributions of vibration frequencies is discussed.

本文基于结合精确积分法（PIM）和自由度变换技术的比例边界有限元法（SBFEM），对具有多个切口的单层和多层复合板进行自由振动分析。它适用于各种形状的板，包含心形，圆形和其他复杂的切口。关键方程是在二维模型的基础上制定的，离散化仅以三个平移位移分量为基本未知量进行。在所提出的技术中应用了高阶光谱元素来精确模拟切口的弧形边界。通过SBFEM的重要半解析特征，可以精确地探索横向自由振动的响应。控制方程的推导严格遵循3D弹性理论，无需引入任何假设。SBFEM关键方程的一般解采用矩阵指数的形式，该矩阵指数由PIM计算。作为一种高度精确的方法，引入了PIM以从解析指数矩阵创建全局刚度矩阵，从而可以确保特征解具有足够的精度。借助动能公式的方法论，构造了多孔板结构的整体质量矩阵。对于薄板，采用自由度变换来降低特征值方程的维数，从而提高计算效率。带有各种切口的柔性正方形和圆形板的数值示例表明，通过开发的方法预测的固有频率与其他方法和精确解所预测的固有频率之间实现了极好的一致性。此外，讨论了边界条件，倾斜角，厚度与长度之比和切口尺寸对振动频率分布的影响。